Intersection of more than 2 mesh objects
There is a way to do this. It is not ideal, but it works and is also non-destructive. Select one of the meshes that is part of the intersection. Add a Boolean modifier to it, choose one of the other objects as the Object in the Boolean modifier. Copy that modifier and chose the other mesh as the Union Object this time. After yo do this there will be a vertex at the intersection 


Select one of the meshes, any will do (A)
Add a Boolean modifier to it:


Operation: Union
Object: one of the other ones (B)

Copy the Boolean modifier


Object: the other one (C)

Optional: If you would like to use the intersection in edit mode to move around mesh components. If all you want to do is to get the intersection just add the empty


add an empty, plain axis will do fine
snap the empty to the intersection: Set the snapping type to vertex. The empty acts as a vertex in this case
in edit mode snap the geometry to the empty if you want to.



Note: You can delete the modifiers when you no longer need them.